Answer:
3 seconds is the time when the object hits the ground.
Step-by-step explanation:
Given the height of a free falling object at time t can be found using the function is given by:
[tex]h(t)=-12t^2+36t[/tex] ....[1]
where,
h(t) is the height in feet
t is the in seconds.
We have to find the time when the object hits the ground.
⇒h(t) = 0
Substitute this in [1] we have;
[tex]-12t^2+36t =0[/tex]
⇒[tex]12t^2-36t = 0[/tex]
⇒[tex]12t(t-3) = 0[/tex]
⇒t = 0 and t = 3
Since, time cannot be 0.
⇒t = 3 seconds
Therefore, the time when the object hits the ground is, 3 seconds
Hey can you please help me posted picture of question
The table below shows a correct representation that 15 pounds (lb) of sugar cost $3: lb lb lb lb lb lb lb lb lb lb lb lb lb lb lb $1 $1 $1
Answer:
true
Step-by-step explanation:
If you roll a fair six-sided die and a fair four-sided die, what is the probability that neither die shows a 1?
Let f(x) = -6x + 3 and g(x) = 5x + 4. Find f*g and state its domain.
-18x2 - 39x + 20; all real numbers except x = 1
-30x2 - 9x + 12; all real numbers
-18x2 - 39x + 20; all real numbers
-30x2 - 9x + 12; all real numbers except x = 4
at the market,8 apples cost $4.How much do 9 apples cost?
-1+7n
A. Quadratic monomial
B. Quadratic trinomial
C. Linear binomial
D. fifth degree binomial
E. none
Minimze the product of a positive rational number and a negative rational number, given that the positive number is exactly 8 greater than the negative number. what is the final product?
an organization surveyed a random sample of their employees about their new vacation policy. Out of the employees surveyed, 83% rated the vacation policy as "delightful" with a margin of error of ±2% and a confidence interval of 95%. What does the margin of error imply?
Answer:
Given is:
Out of the employees surveyed, 83% rated the vacation policy as "delightful" with a margin of error of ±2% and a confidence interval of 95%.
±2% means plus 2% from 83% and minus 2% from 83%, making the interval between 81% and 85%.
In general the margin of error tells that, how many percentage points the results will differ from the real population value. A small margin of error shows trustworthy results whereas a large margin of error means the results are not accurate.
Therefore, it can be concluded, with 95% confidence, that between 81% and 85% of all employees will rate the vacation policy as "delightful."
You help build a new play center at a daycare. The play center has a tunnel for the children to climb through. You are painting the outside of the tunnel. Find the approximate surface area of the outside of the tunnel so you know how much area you need to paint. Use 3.14 to approximate pi.
Your salary is $25,000 you just received a 2.5% pay increase for the year. What is your new salary?
identify the two rational numbers. A) √2 B) 1.01 C) 1.010010001... C) -2/5
We have that for the Question "identify the two rational numbers. " it can be said that
Option B,C,D is rational
From the question we are told
identify the two rational numbers.
A)√2
B) 1.01
C) 1.010010001...
D) -2/5
Generally
Rational number are real number that exist is a form where the denominators are not zero
Therefore
A)√2 this is an irratioanl number as its \pm 1
B) 1.01 Rational
C) 1.010010001... rational
D) -2/5 rational
Hence
Option B,C,D is rational
For more information on this visit
https://brainly.com/question/19007362?referrer=searchResults
identify the slope and Y- intercept of the graph of the equation.Then graph the equation, Y = - 5/4X + 1
8x+6=5x+9
[tex]8x + 6 = 5x + 9[/tex]
Final answer:
To solve the equation 8x + 6 = 5x + 9, subtract 5x from both sides to get 3x + 6 = 9, then subtract 6 from both sides to get 3x = 3. Finally, divide by 3 to find x = 1.
Explanation:
The equation given is 8x + 6 = 5x + 9. To solve for x, you first want to get all terms containing x on one side and the constants on the other. This is achieved through the use of addition or subtraction. From LibreTexts™, we know that addition or subtraction of the same number on both sides of an equation maintains equality. So, subtract 5x from both sides:
8x + 6 - 5x = 5x + 9 - 5x
3x + 6 = 9
Next, you subtract 6 from both sides to isolate the x term:
3x + 6 - 6 = 9 - 6
3x = 3
Now, you divide both sides by 3, a step also indicated by LibreTexts™ as multiplication or division by the same number maintains the equation's balance:
3x / 3 = 3 / 3
x = 1
The solution to the equation is x = 1.
find (f o g)(2) and (f+g)(2) when f(x)=1/x and g(x)=4x+9
To find (f o g)(2), substitute the value of g(2) into f. To find (f+g)(2), find f(2) and g(2) separately, then add them together.
Explanation:To find (f o g)(2), we need to first find g(2), and then substitute that value into f. To find g(2), we substitute 2 into the expression for g(x). g(2) = 4(2) + 9 = 8 + 9 = 17. Now, we substitute 17 into the expression for f(x), which is 1/x. (f o g)(2) = f(g(2)) = f(17) = 1/17.
To find (f+g)(2), we first need to find f(2) and g(2) separately. f(2) = 1/2, and g(2) = 17. Now, we add them together. (f+g)(2) = f(2) + g(2) = 1/2 + 17 = 1/2 + 34/2 = 35/2 = 17.5.
A bookstore costs $75 a day to keep open, and it spends $11 for each book that it sells. If each book sells for $16, what is the break-even point for this bookstore?
Answer:c=11n+75
Step-by-step explanation:
Q9 Q6.) Write an equation for intersection l₂ that keeps traffic moving.
What is the measure of ∠N?
2 + 3 × 16 − 2 × 21 − 3
Final answer:
To solve the expression 2 + 3 × 16 − 2 × 21 − 3, we use the order of operations rule, starting with multiplication to get 48 and 42, followed by addition and subtraction to arrive at the final answer of 5.
Explanation:
The student's question requires us to solve a mathematical expression using the correct order of operations. In the expression 2 + 3 × 16 − 2 × 21 − 3, we need to follow the BIDMAS/BODMAS/PEMDAS rule (Brackets, Indices/Orders, Division and Multiplication, Addition and Subtraction). This rule ensures that we perform multiplication and division before addition and subtraction.
First, we calculate the multiplication parts: 3 × 16 and 2 × 21.
3 × 16 = 48
2 × 21 = 42
Substituting these into the original expression gives us:
2 + 48 − 42 − 3
Next, we perform the addition and subtraction in order from left to right:
2 + 48 = 50
50 − 42 = 8
8 − 3 = 5
So, the expression simplifies to the number 5.
A marble is drawn at random first from a jar containing four black and four white marbles, and then from a jar containing six black and two white marbles. What is the probability of drawing two black marbles?
[tex] |\Omega|=8\cdot8=64\\
|A|=4\cdot6=24\\\\
P(A)=\dfrac{24}{64}=\dfrac{3}{8}=37.5\% [/tex]
Answer:
the answer is 37.5% Hope this helps!
The sum of two numbers is 43 . The larger number is 11 more than the smaller number. What are the numbers
a + b = 43 (the sum of two numbers is 43)
(a +11) = b (he larger number is 11 more than the smaller number)
so:
a + b = 43
a + (a + 11) = 43
a + a + 11 = 43
2a = 43 - 11
2a = 32
a = 16
now:
a + b = 43
16 + b = 43
b = 43 - 16
b = 27
that is:
a = 16
b = 27
--------------------------
checking:
b - a = 11
27 - 16 = 11 (TRUE)
Factor x3 + 2x2 + x completely
Answer:
x(x+1)²
Step-by-step explanation:
x is a common factor to all terms so the first step is to factor it out:
... x(x² +2x +1)
The quadratic factor is recognizable as the square (x+1)², so the factoring is ...
... x(x +1)²
Answer:
Step-by-step explanation:x(x+1)2
write in short; × + 2× + 13×
Ken started saving for retirement at age 35 with plans to retire at age 70. He invested an average of $600 per month in various securities, with an average annual return of 5% adjusted for inflation. Assuming monthly compounding, how much has Kent saved at the start of retirement
A: $54,192.18
B: $825,655.45
C: $499,355.18
D: $681,655.46
what is the median number for the numbers 4,8,10,5,9?
Hello There!
Median: The middle number when all the numbers are listed in oder from least to greatest.
To find the median, place the numbers in order from least to greatest.
In this case, the numbers would be 4, 5, 8, 9, 10
The middle number would be 8 so the median for this set of numbers is 8.
Jordan worked out at a gym for 2 hours. His workout consisted of stretching for 21 minutes, jogging for 45 minutes, and lifting weights for the remaining amount of time. What percentage of Jordan’s workout was spent lifting weights?
2,5,11,20 32,47 what is the next number in the series
The next number in the series is 65. To identify the pattern in the given series and find the next number, let's look at the differences between consecutive terms.
5 - 2 = 3
11 - 5 = 6
20 - 11 = 9
32 - 20 = 12
47 - 32 = 15
As we observe, the differences between consecutive terms are increasing by 3 each time. So, to find the next difference, we add 3 to the last difference:
15 + 3 = 18
Now, to find the next number in the series, we add this difference to the last number in the series:
47 + 18 = 65
Therefore, the next number in the series is 65.
To know more about series:
https://brainly.com/question/30241975
#SPJ6
A rubber ball dropped on a hard surface takes a sequence of bounces, each one 4/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled at the time when it hits the surface for its fifth bounce?
A) 28 77/125 feet
B) 49 1/25 feet
C) 57 29/125 feet
D) 59 29/125 feet
Answer:
The answer is 57 29/125 feet ⇒ answer (C)
Step-by-step explanation:
∵ The ball dropped from a height 10 feet
∴ The vertical distance = 10 feet
∵ It bounces 4/5 as high as the preceding one
∴ 1st bounce = 10 × 4/5 = 8 (move down another 8)
∴ The vertical distance = 8 + 8 = 16 feet
∴ 2nd bounce = 8 × 4/5 = 6.4 (move down another 6.4)
∴ The vertical distance = 6.4 + 6.4 = 12.8 feet
∴ 3rd bounce = 6.4 × 4/5 = 5.12 (move down another 5.12)
∴ The vertical distance = 5.12 + 5.12 = 10.24 feet
∴ 4th bounce = 5.12 × 4/5 = 4.096 (move down another 4.096)
∴ The vertical distance = 4.096 + 4.096 = 8.192 feet
∵ The ball will hit the surface to make the 5th bounce
∴ The total vertical distance is :
10 + 16 + 12.8 + 10.24 + 8.192 = 57.232 = 57 29/125
Another way:
* We can use the formula of geometric sequence with
1st bounce distance (a) = 8 + 8 = 16 and ratio (r) = 4/5
and number of bounces (n) = 4 (hit the surface for its 5th bounce)
∵ [tex]S_{n}=\frac{a(1-(r^{n}))}{1-r}[/tex]
∴ [tex]S_{4}=\frac{16(1-(\frac{4}{5})^{4})}{1-\frac{4}{5}}=47\frac{29}{125}[/tex]
* Then we must to add the 10 feet
(the ball dropped from height 10 feet)
∴ The total vertical distance = 10 + 47 29/125 = 57 29/125 feet
A rectangular prism has a volume of 96ft3. The area of the base is 24ft2. What is thw height of the prism? answer soon please
hey can you please help me posted picture of question
Simplify
cosx ( tanx+cotx)
Final answer:
The expression cosx (tanx+cotx) simplifies to sinx+cosx by using trigonometric identities and recognizing that tanx and cotx can be expressed in terms of sinx and cosx, allowing terms to cancel out.
Explanation:
To simplify the expression cosx (tanx+cotx), we need to use trigonometric identities. Recall that tanx = sinx/cosx, and cotx = cosx/sinx. Therefore, when we multiply cosx by tanx, the cosx in the numerator and denominator will cancel out, leaving us with sinx. Similarly, when we multiply cosx by cotx, sinx in the numerator and denominator will cancel out, leaving us with cosx.
So the simplification process will look like this:
cosx * tanx = sinx
cosx * cotx = cosx
Thus, cosx (tanx+cotx) = sinx+cosx.
This is the simplified form of the expression given. It's important to remember that trigonometric identities are a powerful tool in simplifying expressions involving trigonometric functions.